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Just a note

All of these observations were randomly selected, with replacement, from a population of two zeros and a single one. By replacing each observation, immediately it was taken, samples of this very finite population behaved as if it were infinitely large.

The red lines show the results were we to take an extremely large number of samples - and show how the sum of 8 observations would vary purely as a result of random selection.

Notice that, aside from our independent random selection, these samples were subject to no other source of variation.